Question

For \(f(x)=4x^2+1\) and \(g(x)=\frac{1}{x+2}\), which formula represents \((g\circ f)(x)\)?

Options

• \(\frac{1}{4x^2+3}\)

• \(\frac{1}{4x^2+1}\)

• \(\frac{4}{(x+2)^2}+1\)

• \(4\left(\frac{1}{x+2}\right)^2+1\)

Answer 1

Substitute \(f(x)=4x^2+1\) into \(g\): \(g(f(x))=\frac{1}{(4x^2+1)+2}\). Therefore, \((g\circ f)(x)=\frac{1}{4x^2+3}\).